**Educational Content: Statistical Hypothesis Testing****Data on Soda Can Weights:**The table below summarizes data on the weights (in pounds) of the contents of cans of diet soda versus cans of regular soda. Assume that the two samples are independent random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. A 0.05 significance level is used for the hypothesis test.| | Diet (μ₁) | Regular (μ₂) ||----------------|-----------|--------------|| Sample size (n)| 33 | 33 || Mean (x̄) | 0.79376 lb| 0.80961 lb || Standard Deviation (s) | 0.00435 lb | 0.00742 lb |**Hypothesis Test (Part a):****Objective:**Test the claim that the mean weight of the contents of diet soda cans is less than the mean weight of the contents of regular soda cans.**Hypotheses:**- **Null Hypothesis (H₀):** μ₁ = μ₂- **Alternative Hypothesis (H₁):** μ₁ < μ₂**Options for Null and Alternative Hypotheses (Choose the correct one):**- A. - H₀: μ₁ = μ₂ - H₁: μ₁ > μ₂- B. - H₀: μ₁ = μ₂ - H₁: μ₁ ≠ μ₂- C. - H₀: μ₁ ≠ μ₂ - H₁: μ₁ < μ₂- **D.** - H₀: μ₁ = μ₂ - H₁: μ₁ < μ₂**Conclusion:**Select option D, as it correctly represents the null and alternative hypotheses for testing if the mean weight of diet soda is less than that of regular soda.

Answered: Image /qna-images/answer/fa1bf301-62a7-4ec0-903f-fbd0fc172fbf.jpg

Answered: Data on the weights (lb) of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Data on the weights of the contents of cans of diet soda versus the contents of regular soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts a and b below. Use a 0.5 significance level for both. A. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? The test statistic, t, is: (round to two decimal places as needed)
Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: M₁ μ₂ OC. Ho: H₁ H₂ H₁: H₁
2. A teacher is analyzing these class results for three history tests. The results of all three tests are normally distributed. Test 1 2 3 Mean (u) 85 85 75 a. Describe and compare the normal curves for tests 1 and 2. b. Compare the normal curves for tests 1 and 3. 3 Standard Deviation (o) Jasmine's Mark μ + 2σ μ – 1.50 μ +3.50 2.5 4.9 c. Determine Jasmine's marks on each test, given the information. Round to the nearest percent Test 1 2.5 Jasmine's Mark (%)
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Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Diet Regular μ μ1 μ2 n 34 34 x 0.79146 lb 0.81544 lb s 0.00437 lb 0.00752 lb A. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. H0: μ1≠μ2 H1: μ1<μ2 B. H0: μ1=μ2 H1: μ1<μ2 C. H0: μ1=μ2 H1: μ1>μ2 D. H0: μ1=μ2 H1: μ1≠ The test statistic, t, is ______.(Round to two decimal places as needed.) B. Construct a confidence interval…
Use the attached image to answer the question: Use the data above to construct a bivariate table and explore if there is an association between one’s education and attitudes toward cohabitation. Is there an association? Describe the pattern of association. Assuming that this is a random sample, test a hypothesis (use α = 0.01) that there is an association between one’s education and attitudes toward cohabitation in the population. Show all your work (state the hypotheses, find the critical value, compute the test statistics, state a conclusion) and write one sentence summarizing the results. (Extra-credit: find the p-value). Is this association weak, moderate or strong? Compute and interpret the appropriate statistic.
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The number of calories in a 12-oz serving of randomly selected regular and lite beers is recorded and the summarized statistics is below. Is there sufficient evidence to conclude that the mean number of calories for lite beers is the same as that for the regular beers? Use alpha of .1. Assume the variables are approximately normally distributed. Variable N Mean StDev regular 25 140.08 19.56 lite 23 122.90 18.19
Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.10 significance level to test for a difference between the measurements from the two arms. What can be concluded? Right arm 142 132 127 137 130 D Left arm 174 172 184 137 147 O A. Ho: Hd =0 B. Ho: Ha 0 H1: Hd =0 %3D OC. Ho: Hd = 0 H1: Hd 0 Identify the test statistic. (Round to two decimal places as needed.) t= Identify the P-value. P-value = (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test?
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A researcher takes sample temperatures in Fahrenheit of 17 days from New York City and 18 days from Phoenix. Test the claim that the mean temperature in New York City is different from the mean temperature in Phoenix. Use a significance level of α=0.05. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. New York City Phoenix 99 94.2 95.5 72 93.2 86.8 102 122.1 85.4 114.4 80 94.7 86.4 89.7 75.4 104.7 79.5 77.6 83.4 106.8 64.3 98.6 65.5 91.5 87.7 82 104 97.7 74.3 64.9 59.5 82 82.8 72 116.2 The Hypotheses for this problem are: H0: μ1 = μ2 H1: μ1μ2 Find the p-value. Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. p-value =

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